Analytical study of oscillatory flow of Maxwell fluid through a rectangular tube

Abstract

In the present study, the oscillatory flow of Maxwell fluid in a long tube with a rectangular cross section is considered. The analytical expressions for velocity profile and phase difference are obtained, and particularly, the singularities of the exact solution are discussed. Furthermore, the convenient expressions of velocity and phase difference are given explicitly for calculations. The effects of the relaxation time and Deborah number on the velocity profile and phase difference are discussed numerically and graphically.